sodium    MARCO GRILLI

                                                                foto-marco-grilli

CONDENSED MATTER PHYSICS

Reception time
MONDAY 14-15 UFFICIO 147 EDIFICIO MARCONI

The course starts on Wednesday 25/09/2024 in aula Amaldi Edificio Marconi


THE STUDENTS OF PROF. GRILLI'S CHANNEL ARE KINDLY REQUESTED TO SUBSCRIBE THE CLASSROOM PLATFORM OF THE COURSE FOR ANY FURTHER ANNOUNCEMENT. THE SUBSCRIPTION CODE IS: 

ccnyn6z



 A.A: 2024/25. Teacher Marco Grilli
Lecture schedule:
Wednesday 8-10 (Aula Amaldi)
Thursday12-14 (Aula Cabibbo)
Friday 15-16 (Aula Cabibbo)


Exam dates:
23/01/2025  at 14:00 written exam (Aula Amaldi, Marconi Blg)

30/01/2025  at  09:00 oral exam (Prof. Grilli office, room 147, Marconi Blg)

06/02/2025 at  09:00 extra oral exam (Prof. Grilli office, room 147, Marconi Blg)
[only for QUARMEN AND LA SCALA students]


13/02/2025  at 14:00 written exam (Aula Amaldi, Marconi Blg)

24/02/2025  at  09:00 oral exam (Prof. Grilli office, room 147, Marconi Blg)

26/06/2025  at 09:00 written exam (Aula Amaldi, Marconi Blg)

01/07/2025  at  09:00 oral exam (Prof. Grilli office, room 147, Marconi Blg)

17/07/2025  at 14:00 written exam (Aula Amaldi, Marconi Blg)

22/07/2025  at  09:00 oral exam (Prof. Grilli office, room 147, Marconi Blg)

04/09/2025  at 14:00 written exam (Aula Amaldi, Marconi Blg)

22/07/2025  at  09:00 oral exam (Prof. Grilli office, room 147, Marconi Blg)


Program

Crystal structures and Bravais lattice. Reciprocal lattice. Diffraction and solid crystals, structure factor. Born-Oppheneimer approximation. Lattice vibrations, phonons, specific heat (Einstein's and Debye's model, density of states). Electrons in solids, Bloch's theorem,. Band structure. Tightly and weakly bound electrons. Holes and effective mass. Electrons in metals and interaction with an electromagnetic field (dielectric response, metal transport properties): Drude's and Sommerfeld's models. Intrinsic and extrinsic semiconductors. Temperature dependence of charge carrier density.

Adopted texts

N.W. Ashcroft, N.D, Mermin, `Solid State Physics', Holt-Saunders Int. Ed. 1981

C. Kittel, `Introduction to Solid Sate Physics', Wiley, 2004

J. M. Ziman, `Principles of the Theory of Solids', Cambridge University Press, 1979

Prerequisites

The course relies on the following prerequisites:
1. CLASSICAL MECHANICS reference text: H. Goldstein, C. P. Poole, and J. L. Safko Classical Mechanics, Addison-Wesley chapter 1 Survey of elementary principles - mechanics of a particle - mechanics of a system of particles - contraints - D'Alambert's principle and Lagrange's equations chapter 6 Oscillations - formulation of the problem - the eigenvalue equation and the principal axis transformation - frequencies of free vibration and normal coordinates chapter 8 The Hamilton equations of motion - Legendre transformations and the Hamilton equations of motion chapter 9 Canonical transformations - the equations of canonical transformations - Poisson brackets - Liouville's theorem
2. CLASSICAL ELECTROMAGNETISM reference text: D. Halliday, R. Resnick, and K. S. Crane Physics - part II, John Wiley & sons chapter 25 Electric charge and Coulomb's law - electric charge - conductors and insulators - Coulomb's law - continuous charge distributions - conservation of charge chapter 26 The electric field - the electric field - the electric field of point charges - the electric field of continuous charge distributions chapter 27 Gauss' law - the flux of the electric field - Gauss' law chapter 28 Electric potential energy and potential - electric potential energy - electric potential - calculating the potential from the field - potential due to point charges - potential due to continuous charge distributions - calculating the field from the potential - equipotential surfaces - the potential of a charged conductor chapter 29 The electric properties of materials - types of materials - a conductor in an alectric field - ohmic materials - Ohm's law - an insultatori in an electric field chapter 30 Capacitance - capacitors - capacitance chapter 31 DC circuits - electric current - electromotive force chapter 32 The magnetic field - the magnetic force on a moving charge - circulating charges - the Hall effect
3. QUANTUM MECHANICS reference text: J. J. Sakurai Modern Quantum Mechanics, Addison-Wesley chapter 1 Fundamental concepts - kets, bras, operators - base kets and matrix representation - measurements, observables, and uncertainty relations - position, momentum, and translation - wave functions in position and momentum space chapter 2 Quantum dynamics - time evolution and the Shroedinger equation - the Shroedinger versus the Heisenberg picture - simple harmonic oscillator - Schroedinger's wave equation chapter 3 Theory of angular momentum - rotations and angular momentum commutation relations - spin 1/2 systems and finite rotations - eigenvalues and eigenstates of angular momentum - orbital angular momentum - addition of angular momenta chapter 4 Symmetry in quantum mechanics - symmetries, conservation laws, and degeneracies - discrete symmetries, parity, or space inversion - lattice translation as a discrete symmetry - the time-reversal discrete symmetry chapter 5 Approximation methods - time independent perturbation theory: non degenerate case - time independent perturbation theory: the degenerate case
4. STATISTICAL MECHANICS reference text: K. Huang Statistical Mechanics, John Wiley & sons chapter 6 Classical statistical mechanics - the postulate of classical statistical mechanics - microcanonical ensemble - derivation of thermodynamics - equipartition theorem - classical ideal gas chapter 7 Canonical ensemble and grand canonical ensemble - canonical ensemble - energy fluctuations in the canonical ensemble - grand canonical ensemble - density fluctuations in the grand canonical ensemble - the chemical potential - equivalence of the canonical ensemble and grand canonical ensemble chapter 8 Quantum statistical mechanics - the postulate of quantum statistical mechanics - ensembles in quantum statistical mechanics - the ideal gases: micro canonical ensemble - the ideal gases: grand canonical ensemble chapter 11 Fermi systems - the equation of state of an ideal Fermi gas chapter 12 Bose systems - photons - Bose-Einstein condensation
5. ATOMIC AND MOLECULAR PHYSICS reference text: B. H Bransden & C. J. Joachain Physics of atoms and molecules, Longman Scientific & Technical chapter 3 One-electron atoms - the Scheoedinger equation for one-electron atoms - energy levels - the eigenfunctions of the bound states chapter 6 Two-electron atoms - the Scheoedinger equation for two-electron atoms - spin wave functions and the role of the Pauli exclusion principle - level scheme of two-electron atoms chapter 7 Many-electron atoms - the central field approximation - the periodic system of the elements chapter 9 Molecular structure - general nature of molecular structure - the Born-Oppenheimer separation for diatomic molecules - electronic structure of diatomic molecules - the structure of polyatomic molecules
Study modes

The course includes lectures on the theory (amounting to approximately 2/3 of the total number of hours dedicated to lecturing), alternated with tutoring sessions (amounting to approximately 1/3 of the total number of hours dedicated to lecturing), during which the methods to solve problems and exercises of the kinds that can be assigned in a written exam are treated.
Frequency modes

Attendance to the lectures is not mandatory but strongly recommended.

Exam modes
There are two mid-term assessment tests during the course (lasting two hours each). If both tests are passed with a score of at least 15/30 and an average of not less than 18/30, the student is exempted from the written test for the entire academic year.
There are 5 complete calls (written and oral): two in the January/February session, two in the June/July session and one in the September session.
The written test (lasting three hours) includes two problems, each one divided into several questions. The written test is passed with a score of no less than 18/30 and is valid for the session in which it was taken.
The oral exam consists of an interview on the most relevant topics presented in the course. To pass the exam, the student must be able to present arguments and repeat calculations discussed and explained during the course. The student will be asked to apply the methods learned during the course to exercises or to examples and situations similar to those that were discussed in the course.
The evaluation takes into account:
- Correctness and completeness of the concepts discussed by the student;
- clarity and rigor of presentation;
- analytical development of the theory;
- problem-solving skills (method and results).

The final exam grade is determined by the average between the written score (or the average of the mid-term assessment tests) and the oral test score.



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Crystal structures, Bravais lattices [AM ch.4] -Reciprocal lattice  [AM ch. 5] -Diffraction from crystals, structure factor [AM Ch. 6]
-Born-Oppenheimer approximation [Ziman p. 200, Bassani, notes]- Lattice vibrations, phonons -Specific heat (Einstein and Debye models, density of states) [AM-Ch. 22 p.421-443 and ch. 23]
- Electrons in solids, Bloch theorem - Electronic bands - Nearly-free electrons - The tight-binding method  -  [AM ch. 8-10]. The concepts of holes and effective mass.
- Electrons in metals and interaction with the electromagnetic field (Dielectric function, transport properties of metals): Drude model and Sommerfeld model [AM ch. 1,2]. Semiclassical model [AM Ch. 12].
- Intrinsic and extrinsic (doped) semiconductors - T dependence of the number of charge carriers [AM cap. 28]

Optional topics:
Boltzmann equation (relaxation-time approx.)  [Ziman, Sec. 7.1,7.2]
Physics of the p-n junction and applications to devices.
[AM ch. 29 p. 589-600].

Useful topics: AM  B, C, D, E, F, L Appendices.

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References
- [AM]N.W. Ashcroft, N.D, Mermin, `Solid State Physics`, Holt-Saunders Int. Ed. 1981.
- C. Kittel, `Introduzione alla Fisica dello Stato Solido`, Ed. CEA, 2008.
- J.M. Ziman, `Principles of the Theory of Solids', Cambridge University Press (1979)
- [BG] F. Bassani e U. M. Grassano, FISICA DELLO STATO SOLIDO, Bollati Boringhieri editori

26/09/24

Bravais Lattices  (A-M ch 4)

27/09/24

Bravais Lattices  (A-M ch 4)

02/10/24

Bravais Lattices  (A-M ch 4)

03/10/24

Reciprocal lattice (A-M ch 5)

04/10/24

X-ray scattering, Bragg and von Laue (A-M ch 6)

09/10/24

equivalence Bragg-von Laue, structure factors,
selection rules

10/10/24

Methods of X-ray scattering, exercise on Diffraction

11/10/24

Exercise on Diffraction

16/10/24

second demo von Laue scatt. (libro Bassani)

17/10/24

Periodic Boundary conditions and the Bloch
Theorem (1st demo ch. 8 A-M)

18/10/24

The Bloch Theorem (2nd demo ch. 8 A-M)

23/10/24

Recap on Bloch Theorem and exercise on
diffraction (Ch 8 A-M)

24/10/24

Meaning of the band quantum number,  (Ch 8 A-M)

25/10/24

Electron density of states,  general definition
and calculation  (Ch 8 A-M)

30/10/24

Nearly Free Electron, NFE  (Ch. 9 A-M) case
of non-degenerate Bloch states

31/10/24

Nearly Free Electron, NFE  (Ch. 9 A-M) case
of degenerate Bloch states

06/11/24

The tight-binding approach  (TBA)

07/11/24

The tight-binding approach, density of states,
example (simple cubic)

08/11/24

Exercise on TBA for 2D lattice without basis.

13/11/24

Exercise on TBA for 2D lattice with basis. T
he effective mass tensor

14/11/24

Velocity of Bloch electrons, example of TBA

15/11/24

Effective electron mass

20/11/24

Transport in metals: Drude model (A-M ch 1)

21/11/24

Drude model: heat conductivity. (A-M ch 1)
Sommerfeld model  (A-M ch 2)

22/11/24

Exercise on TBA for 2D lattice with basis.

27/11/24

failures of the Drude model and quick summary
of Sommerfeld model  (A-M ch 1-2)

28/11/24

Assumptions of the semiclassical model (A-M ch. 12)

29/11/24

The semiclassical model

04/12/24

Exercises on tight-binding model

05/12/24

The Born-Oppenheimer approximation

06/12/24

Mid-term test

11/12/24

phonons in 1D lattice

12/12/24

phonons in 2D square lattice

13/12/24

The Debye and the Einstein model for phonon
specific heat

18/12/24

exercises on phonons

19/12/24

exercises on phonons

20/12/24

exercises on phonons semiconductors

08/01/25

Intrinsic  semiconductors

09/01/25

Extrinsic semiconductors

10/01/25

Exercises on semiconductors

15/01/25

Exercises on semiconductors

 

Last Update November 2024